Differential Calculations - Casio FX-9750G plus User Manual

3-2 Differential Calculations

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To perform differential calculations, first display the function analysis menu, and
then input the values shown in the formula below.
d dx f(x)
/ )
2(
d/dx ( f (x), a, Ax) ⇒ ––– f (a)
The differentiation for this type of calculation is defined as:
f '(a) = lim –––––––––– –––
Ax→0
In this definition, infinitesimal is replaced by a sufficiently small A
in the neighborhood of f ' (a) calculated as:
f (a + Ax) – f (a)
–––––––––– –––
f '(a)
In order to provide the best precision possible, this unit employs central difference
to perform differential calculations. The following illustrates central difference.
a
The slopes of point
y = f(x)
are as follows:
f (a + Ax) – f (a)
–––––––––– ––– = ––– , –––––––––– ––– = –––
Ax
y x is called the forward difference, while ∇
In the above, A /A
difference. To calculate derivatives, the unit takes the average between the value
y x and ∇ y x
of A /A /∇ , thereby providing higher precision for derivatives.
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a x
, ,A )
Increase/decrease of
Point for which you want to determine the derivative
d
dx
f (a + Ax) – f (a)
Ax
Ax
A
A
A A
A
A
a + x
and point , and of point
A
y
f (a) – f (a – Ax)
A
Ax Ax
[OPTN]-[CALC]-[d/dx]
x
x
, with the value
A
a a – x
and point in function
A
∇ y
∇x
y x
/∇ is the backward
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